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Discussion questions on systems of linear equations

Please provide an answer to the following questions below that contains 250 to 300 words each.

1.By looking at two linear equations, how can you tell that the corresponding lines are parallel, the same graph, or intersecting lines? How many solutions does each possibility have and why is that? Show examples for each possible situation.

2.Is there a difference between solving a system of equations by the algebraic method and the graphical method? Why? What are the advantages and disadvantages of each?

3.Write 250-300 words comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why. Support your answer by appropriate examples.

Solution Preview

Hi,

Please find the solutions/explanations attached herewith.

Please provide an answer to the following questions below that contains 250 to 300 words each.

1. By looking at two linear equations, how can you tell that the corresponding lines are parallel, the same graph, or intersecting lines? How many solutions does each possibility have and why is that? Show examples for each possible situation.

Solution:

PARALLEL LINES:

If two equations have same slopes then the lines are parallel.

Let us take example

y = 3x + 7

and y = 3x - 5

We can see that the slope of both the lines is 3. Therefore, lines are parallel.

These types of system of equations have NO Solution as they don't have any common point which satisfies both the equations.

SAME GRAPH:

The equations have same graph when both the equations are same.

Let us take one example to illustrate it.

x + y = 2
2x + 2y = 4

We can see that we can get second equation by multiplying first equation by 2.

Or just divide second equation by 2, we will first equations, therefore they have same graph. These types of system of equations have infinity many solutions as if we give any different values to one variable we will get corresponding for other variable.

INTERSECTING LINES:

If the system of linear equations are not of the above two types then the lines are intersecting lines. That is if neither the equations are of parallel lines nor have same graph then the lines are intersecting lines.

Let us take the example
x + y = 1
x - y = 3

The slope of first line is -1 and slope of second line is 1. ...

Solution Summary

Detailed explantions to all the quesions is provided.

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